Abstract
We initiate a systematic study of ‘t Hooft anomalies in Galilean field theories, focusing on two questions therein. In the first, we consider the non-relativistic theories obtained from a discrete light-cone quantization (DLCQ) of a relativistic theory with flavor or gravitational anomalies. We find that these anomalies survive the DLCQ, becoming mixed flavor/boost or gravitational/boost anomalies. We also classify the pure Weyl anomalies of Schrödinger theories, which are Galilean conformal field theories (CFTs) with z=2z=2. There are no pure Weyl anomalies in even spacetime dimension, and the lowest-derivative anomalies in odd dimension are in one-to-one correspondence with those of a relativistic CFT in one dimension higher. These results classify many of the anomalies that arise in the field theories dual to string theory on Schrödinger spacetimes.
Highlights
Anomalous global symmetries provide one of the most useful handles on non-perturbative field theory
Our results for flavor and gravitational anomalies hold for the string theory embeddings of Schrödinger holography [22,23,24], wherein the NR field theory is obtained by discrete light-cone quantization (DLCQ) together with a holonomy for a global symmetry around the null circle
Suppose we study the NR theory that arises from the DLCQ of a relativistic theory with flavor and/or gravitational anomalies
Summary
Anomalous global symmetries provide one of the most useful handles on non-perturbative field theory. Our results for flavor and gravitational anomalies hold for the string theory embeddings of Schrödinger holography [22,23,24], wherein the NR field theory is obtained by DLCQ together with a holonomy for a global symmetry around the null circle. There have been several attempts [27,28,29] to compute the Weyl anomaly of a non-relativistic free field in 2 + 1-dimensions. This anomaly should satisfy a sort of sum rule. Those authors find that only a massless non-relativistic scalar has an anomaly, and go on to demonstrate that this result remains true to all orders in perturbation theory
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